Recursion is an important concept and a fundamental problem-solving technique in computer science. Studies have reported that it is considered a very difficult concept for students to learn and teachers to teach, and students have many misconceptions about recursion. Tools proposed to overcome these difficulties include visualization and algorithm animation. Conceptual models form the basis of methods for teaching recursion and influence the instructional tactics used when teaching it. Conceptual models of recursion have been found to provide a necessary representation for understanding the mechanics of recursion. Several of these models have been proposed, including the Russian dolls model, process tracing model, mathematical induction model, and structure template model. These are not based on a systematic foundation that visualizes the process in terms of flows of the recursive algorithm from the stages of creating (copying) then processing (executing) it. This paper presents such a methodical conceptual picture that describes the recursive process in a precise, visual way that assists in teaching and learning. The new model is illustrated by several examples, including factorial and binary tree traversing.